CCII based fractional filters of different orders

This paper aims to generalize the design of continuous-time filters to the fractional domain with different orders and validates the theoretical results with two different CCII based filters. In particular, the proposed study introduces the generalized formulas for the previous fractional-order analysis of equal orders. The fractional-order filters enhance the design flexibility and prove that the integer-order performance is a very narrow subset from the fractional-order behavior due to the extra degrees of freedom. The general fundamentals of these filters are presented by calculating the maximum and minimum frequencies, the half power frequency and the right phase frequency which are considered a critical issue for the filter design. Different numerical solutions for the generalized fractional order low pass filters with two different fractional order elements are introduced and verified by the circuit simulations of two fractional-order filters: Kerwin–Huelsman–Newcomb (KHN) and Tow-Tomas CCII-based filters, showing great matching.

[1]  A. Sedra.  Microelectronic circuits , 1982 .

[2]  Ahmed S. Elwakil,et al.  On the Generalization of Second-Order Filters to the fractional-Order Domain , 2009, J. Circuits Syst. Comput..

[3]  K. Biswas,et al.  Performance study of fractional order integrator using single-component fractional order element , 2011, IET Circuits Devices Syst..

[4]  M. Nakagawa,et al.  Basic Characteristics of a Fractance Device , 1992 .

[5]  Rong Chen,et al.  Study of Threshold Setting for Rapid Detection of Multicomponent LFM Signals Based on the Fourth-Order Origin Moment of Fractional Spectrum , 2013, Circuits Syst. Signal Process..

[6]  A.M. Davis,et al.  Microelectronic circuits , 1983, Proceedings of the IEEE.

[7]  Ahmed M. Soliman,et al.  Fractional order filter with two fractional elements of dependant orders , 2012, Microelectron. J..

[8]  Luigi Fortuna,et al.  Fractional Order Systems: Modeling and Control Applications , 2010 .

[9]  Ahmed M. Soliman,et al.  Novel CMOS realizations of the inverting second-generation current conveyor and applications , 2007 .

[10]  Hassen T. Dorrah,et al.  Design of aerospace control systems using fractional PID controller , 2012 .

[11]  K. Salama,et al.  Theory of Fractional Order Elements Based Impedance Matching Networks , 2011, IEEE Microwave and Wireless Components Letters.

[12]  Khaled N. Salama,et al.  Fractional-Order RC and RL Circuits , 2012, Circuits Syst. Signal Process..

[13]  Jeong-Soo Lim,et al.  A modified Chebyshev bandpass filter with attenuation poles in the stopband , 1997 .

[14]  Ahmed S. Elwakil,et al.  Field programmable analogue array implementation of fractional step filters , 2010, IET Circuits Devices Syst..

[15]  Ahmed S. Elwakil,et al.  Fractional-order sinusoidal oscillators: Design procedure and practical examples , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[16]  Ahmed M. Soliman,et al.  A Novel CMOS Realization of the Differential Input Balanced Output Current Operational Amplifier and its Applications , 2005 .

[17]  Kazuhiro Saito,et al.  Simulation of Power-Law Relaxations by Analog Circuits : Fractal Distribution of Relaxation Times and Non-integer Exponents , 1993 .

[18]  Ahmed H. Madian,et al.  CMOS Realization of the Operational Mirror Amplifier , 2008 .

[19]  S. Pennisi,et al.  Low-voltage CMOS current amplifier and its use for high-performance voltage amplification , 2003 .

[20]  Ahmed S. Elwakil,et al.  First-Order Filters Generalized to the fractional Domain , 2008, J. Circuits Syst. Comput..

[21]  Ahmed M. Soliman.  Two integrator loop quadrature oscillators: A review , 2013, Journal of advanced research.

[22]  Yoshiaki Hirano,et al.  Simulation of Fractal Immittance by Analog Circuits: An Approach to the Optimized Circuits , 1999 .

[23]  Khaled N. Salama,et al.  The fractional-order modeling and synchronization of electrically coupled neuron systems , 2012, Comput. Math. Appl..

[24]  Ahmed M. Soliman.  New inverting non-inverting bandpass and lowpass biquad circuit using current conveyors , 1996 .

[25]  Ahmed M. Soliman,et al.  Kerwin-Huelsman-Newcomb circuit using current conveyors , 1994 .

[26]  Ahmed Gomaa Radwan,et al.  Stability and non-standard finite difference method of the generalized Chua's circuit , 2011, Comput. Math. Appl..

[27]  Ahmed M. Soliman,et al.  A CMOS differential difference operational mirrored amplifier , 2009 .

[28]  A. Elwakil,et al.  On the stability of linear systems with fractional-order elements , 2009 .

[29]  Ahmed M. Soliman,et al.  Current conveyor filters: classification and review , 1998 .

[30]  Ahmed S Elwakil,et al.  Fractional-order circuits and systems: An emerging interdisciplinary research area , 2010, IEEE Circuits and Systems Magazine.

[31]  Ahmed M. Soliman,et al.  Mos-C Tow-Thomas Filter Using voltage op Amp, Current Feedback op Amp and Operational transresistance amplifier , 2009, J. Circuits Syst. Comput..

[32]  A. G. Radwan,et al.  Butterworth passive filter in the fractional-order , 2011, ICM 2011 Proceeding.